Unified Model of Ultracold Molecular Collisions James F
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Unified model of ultracold molecular collisions James F. E. Croft, John L. Bohn, Goulven Quéméner To cite this version: James F. E. Croft, John L. Bohn, Goulven Quéméner. Unified model of ultracold molecular collisions. Physical Review A, American Physical Society, 2020, 10.1103/PhysRevA.102.033306. hal-02638676 HAL Id: hal-02638676 https://hal.archives-ouvertes.fr/hal-02638676 Submitted on 28 May 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. A unified model of ultracold molecular collisions James F. E. Croft The Dodd-Walls Centre for Photonic and Quantum Technologies, New Zealand and Department of Physics, University of Otago, Dunedin, New Zealand John L. Bohn JILA, NIST, and Department of Physics, University of Colorado, Boulder, Colorado 80309-0440, USA Goulven Qu´em´ener Universit´eParis-Saclay, CNRS, Laboratoire Aim´eCotton, 91405, Orsay, France A scattering model is developed for ultracold molecular collisions, which allows inelastic processes, chemical reactions, and complex formation to be treated in a unified way. All these scattering processes and various combinations of them are possible in ultracold molecular gases, and as such this model will allow the rigorous parametrization of experimental results. In addition we show how, once extracted, these parameters can to be related to the physical properties of the system, shedding light on fundamental aspects of molecular collision dynamics. I. INTRODUCTION duced long-lived collisional complexes and what the loss mechanism was. However, a subsequent experiment on Ultracold samples of molecules can be exquisitely con- RbCs [12] showed that turning on or off the trapping light trolled at the quantum state level, allowing fundamental that confines the molecules can increase or decrease the physical and chemical process to be studied with un- losses of the molecules. This confirmed the hypothesis of precedented precision. This control has been used to a theoretical study [13] that the non-reactive molecules study state-to-state chemistry with full quantum state first form tetramer complexes, and then the complexes are resolution for all reactants and products [1], to probe the lost due to light scattering in the optical dipole trap. In potential energy surface with exquisite resolution [2, 3], addition, an experiment on chemically reactive ultracold and to study the role of nuclear spins in molecular colli- molecules such as KRb succeeded in directly observing the sions [4, 5], More recently an experiment has managed to corresponding ions of the intermediate complex K2Rb2 [6], probe the intermediate complex of an ultracold ultracold as well as of the products K2 and Rb2 of the chemical reaction [6] as such it is now possible to track the complete reaction. Just as for non-reactive molecules, the trap- chemical process from reactants, through intermediates, ping light has a strong effect on the losses of the reactive to products. molecules as well as on the lifetime of the transient com- plex [14], sharing the same conclusion as [12, 13]. It is Understanding the fundamental physical and chemical therefore clear that any theoretical treatment of ultracold process of ultracold molecular collisions is also impor- molecular collisions must be flexible enough to account tant because ultracold gases are fragile systems, prone for the formation of the complexes. to collisional processes that can transfer their atomic or molecular constituents into untrapped states or else re- These experiments can be described by a model that lease large amounts of kinetic energy, leading to trap loss assumes an absorption probability pabs for any two and heating. A new mechanism for loss in an ultracold molecules that get within a certain radius [15], without molecular gas was proposed [7, 8], namely a half-collision ascribing any particular mechanism to the absorption. process in which the reactant molecules share energy in Energy and electric field dependence of two-body loss rotational and vibrational degrees of freedom, spending a rates are well-fit by the resulting formulas. For exam- long time lost in resonant states of a four-body collision ple, the reactive molecules in the KRb experiment vanish complex rather than promptly completing the collision with unit probability pabs = 1 with or without electric process. This idea of transient complex formation, collo- field [4, 16, 17]. The non-reactive species NaRb and RbCs quially dubbed \sticking", takes on an added significance vanish with probabilities 0:89 [18] and 0:66 [11] respec- for ultracold molecular collisions where the number of tively, in zero electric field. Notably, when an electric available exit channels can be very small compared to the field is applied to NaRb, its absorption probability climbs number of resonant states. to pabs = 1 [10]. Assuming the origin of this loss is due to Initial experiments on non-reactive ultracold molecules, complex formation, the increased loss with electric field such as NaRb [9, 10] and RbCs [11], observed two-body may be attributed to the increased density of accessible collisional losses, even though these species are non- states of the complex and/or coupling of these states to reactive and are in their quantum mechanical ground the continuum scattering channels. It is therefore con- state, so have no available inelastic loss channels. As ceivable that complex formation may be a phenomenon these complexes were not directly observed, it remained that can be turned on or off as desired. an open question whether these experiments have pro- While the influence of light scattering on molecular 2 V collisions is undeniable, it should also be possible for µ complex formation the molecules to be confined in \box" traps, where the molecules remain mostly in the dark, encountering trap- d ping light only at the peripheries of the trap [19]. In this a case, loss due to complex formation would allow a more b, c, ... Inelastic Observed direct probe of the fundamental four-body physics of the ) collision. k, l, m, ... Reactive In this paper we propose a phenomenological model of direct scattering collisional losses, based on the theory of average cross sec- indirect scattering ρ, σ, τ, ... Unobserved tions [20], that encompasses both direct collisional losses and loss due to complex formation. As such this model serves not only to parametrize experimental measure- r ments, but also allows those parameters to be related to r0 the physical properties of the system, potentially shedding light on the dynamics of the molecular complex. FIG. 1. Schematic outlining the various scattering processes and channel labels. Direct and indirect scattering processes are shown by red and blue arrows respectively. The incoming channel is labelled a; inelastic scattering channels that can be II. THEORY observed in an experiment are denoted by roman letters b, c, :::; reactive scattering channels that can be observed in an The theory must be flexible enough to describe the experiment are denoted by roman letters k, l, m, :::; inelastic various outcomes available when two molecules collide. or reactive channels that are unobserved in a given experiment These include elastic scattering of the reactants; inelastic are denoted by letters ρ, σ, τ, ::: Finally a dense forest of scattering, where the reactants emerge with the same resonant states labelled by µ of the collision complex, of, with a mean level spacing d, is shown in the well of the potential. chemical identity but in different internal states; reactive scattering into various product states; and absorption into the collision complex. Moreover, depending on the experiment, the various outcomes of the collision may or may not be observed. Note that, within this model, formation of a collision complex will always be regarded an outcome in and of itself: we do not consider where the on the details of a particular experiment. In some ex- complex ultimately decays to. periments, all the final states can be measured so that there are no channels denoted by greek letters, while in others none of the final states can be measured so that A. Molecular scattering, observed and unobserved there are no channels denoted by roman letters (except processes the incident channel a). In some experiments, inelastic channels are measured but reactive ones are not, or vice versa. Therefore one has to determine which processes To this end, we define a flexible system of notation as are labelled as observed or unobserved processes for a illustrated in Fig. 1. This figure shows schematically the particular experiment of interest. In Sec. II D, we will distance r between two collision partners (which may be detail how these unobserved processes can be gathered reactants or products), and the various possible outcome into an overall, absorption term. channels. Channels whose outcome is observed by a par- ticular experiment are labelled by roman letters while channels whose outcome is unobserved are labelled by The observed and unobserved processes are those that greek letters. The channels labelling observed processes are expected to produce inelastic scattering or chemical are further differentiated as follows. Channels labelled reactions immediately, that is, without forming a collision a, b, c, ::: correspond to the elastic and inelastic chan- complex, shown in Fig. 1 by the red arrow labelled direct nels of the reactants, while channels labelled k, l, m, ::: scattering. Typically, the results of these processes release correspond instead to channels of a different molecular kinetic energy greater than the depth of the trap holding arrangement and correspond to the product channels of the molecules, and hence lead to what we term direct loss.